Your description is striking similar to Fallout and as Fifth said, it can't be Fallout, because of duh... Windows. But the earliest Win95 games used to ship as a dual version with a 16-bit .exe for DOS and another 32-bit .exe for Windows 95.
Was it the first Fallout game from the series?
http://www.mobygames.com/game/window...eShotId,12649/